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 Documentation Ver 1.0.0 August 2011 by
 <a href="http://mmc.geofisica.unam.mx/luiggi">Luis M. de la Cruz</a> <br>
 <a href="http://mmc.geofisica.unam.mx"> GMMC </a> -
 <a href="http://www.geofisica.unam.mx/recnat/"> Depto. de Recursos Naturales </a> -
 <a href="http://www.geofisica.unam.mx"> Instituto de Geof&iacute;sica </a> -
 <a href="http://www.unam.mx"> UNAM </a><br>
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<h1>Examples/03Laplace/hoffman2.cpp</h1>  </div>
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<div class="contents">
<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*</span>
<a name="l00002"></a>00002 <span class="comment"> ***************************************************************************</span>
<a name="l00003"></a>00003 <span class="comment"> *</span>
<a name="l00004"></a>00004 <span class="comment"> * \file   hoffman2.cpp</span>
<a name="l00005"></a>00005 <span class="comment"> * Laplace equation in 2D</span>
<a name="l00006"></a>00006 <span class="comment"> *</span>
<a name="l00007"></a>00007 <span class="comment"> * \par Description</span>
<a name="l00008"></a>00008 <span class="comment"> * This code solves the Laplace equation in two dimensions: </span>
<a name="l00009"></a>00009 <span class="comment"> * \f$ \nabla^2 T = 0\f$. </span>
<a name="l00010"></a>00010 <span class="comment"> * \par</span>
<a name="l00011"></a>00011 <span class="comment"> * This equation is solved in the rectangle</span>
<a name="l00012"></a>00012 <span class="comment"> * interval \f$ [0,1] \times [0,2] \f$. The boundary conditions are ...</span>
<a name="l00013"></a>00013 <span class="comment"> * \par</span>
<a name="l00014"></a>00014 <span class="comment"> *  To compile and run this example type the next commands:</span>
<a name="l00015"></a>00015 <span class="comment"> * \par</span>
<a name="l00016"></a>00016 <span class="comment">   \verbatim</span>
<a name="l00017"></a>00017 <span class="comment">   % make</span>
<a name="l00018"></a>00018 <span class="comment">   % ./hoffman2 \endverbatim</span>
<a name="l00019"></a>00019 <span class="comment"> * </span>
<a name="l00020"></a>00020 <span class="comment"> ***************************************************************************</span>
<a name="l00021"></a>00021 <span class="comment"> *  \author    Luis M. de la Cruz Salas [ Fri Mar 21 12:26:33 GMT 2008 ]</span>
<a name="l00022"></a>00022 <span class="comment"> ***************************************************************************</span>
<a name="l00023"></a>00023 <span class="comment"> */</span>
<a name="l00024"></a>00024 
<a name="l00025"></a>00025 <span class="preprocessor">#include &lt;iostream&gt;</span>
<a name="l00026"></a>00026 <span class="preprocessor">#include &lt;cmath&gt;</span>
<a name="l00027"></a>00027 <span class="preprocessor">#include &quot;Meshes/StructuredMesh.hpp&quot;</span>
<a name="l00028"></a>00028 <span class="preprocessor">#include &quot;Meshes/Uniform.hpp&quot;</span>
<a name="l00029"></a>00029 <span class="preprocessor">#include &quot;Equations/ScalarEquation.hpp&quot;</span>
<a name="l00030"></a>00030 <span class="preprocessor">#include &quot;Schemes/LaplaceScheme.hpp&quot;</span>
<a name="l00031"></a>00031 <span class="preprocessor">#include &quot;Solvers/TDMA.hpp&quot;</span>
<a name="l00032"></a>00032 <span class="preprocessor">#include &quot;Utils/num_utils.hpp&quot;</span>
<a name="l00033"></a>00033 <span class="preprocessor">#include &quot;Utils/inout.hpp&quot;</span> 
<a name="l00034"></a>00034 <span class="preprocessor">#include &quot;Utils/GNUplot.hpp&quot;</span>
<a name="l00035"></a>00035 <span class="keyword">using namespace </span>Tuna;
<a name="l00036"></a>00036 
<a name="l00037"></a>00037 <span class="comment">// Scalar field in two dimension</span>
<a name="l00038"></a>00038 <span class="keyword">typedef</span> TunaArray&lt;double, 2&gt;::huge ScalarField2D;
<a name="l00039"></a>00039 
<a name="l00040"></a>00040 <span class="keywordtype">void</span> exactSolution(ScalarField2D &amp;T, <span class="keywordtype">double</span> hx, <span class="keywordtype">double</span> hy, <span class="keywordtype">double</span> A,
<a name="l00041"></a>00041                    <span class="keywordtype">double</span> dx, <span class="keywordtype">double</span> dy)
<a name="l00042"></a>00042 {
<a name="l00043"></a>00043   <span class="keywordtype">int</span> NI = T.ubound(firstDim);
<a name="l00044"></a>00044   <span class="keywordtype">int</span> NJ = T.ubound(secondDim);
<a name="l00045"></a>00045   
<a name="l00046"></a>00046   <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 1; i &lt; NI; ++i)
<a name="l00047"></a>00047     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 1; j &lt; NJ; ++j) 
<a name="l00048"></a>00048       T(i,j) = A * sinh( PI * (hy - j * dy) / hx ) * sin( PI * i * dx / hx) / sinh( PI * hy / hx);     
<a name="l00049"></a>00049 }
<a name="l00050"></a>00050 
<a name="l00051"></a>00051 <span class="keywordtype">int</span> <a class="code" href="convdiff3_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() 
<a name="l00052"></a>00052 {
<a name="l00053"></a>00053   <span class="keywordtype">double</span> length_x, length_y, Amp;
<a name="l00054"></a>00054   <span class="keywordtype">int</span> num_nodes_x, num_nodes_y;
<a name="l00055"></a>00055   <span class="keywordtype">double</span> tolerance;    
<a name="l00056"></a>00056   <span class="keywordtype">int</span> tdma_iter;
<a name="l00057"></a>00057   <a class="code" href="structTuna_1_1timer.html" title="Struct useful to measure the elapsed time.">timer</a> time;
<a name="l00058"></a>00058   
<a name="l00059"></a>00059 <span class="comment">// Reading data from the input file</span>
<a name="l00060"></a>00060   std::ifstream input_cin (<span class="stringliteral">&quot;input_hoffman&quot;</span>); 
<a name="l00061"></a>00061   input_cin &gt;&gt; length_x;
<a name="l00062"></a>00062   input_cin &gt;&gt; length_y;
<a name="l00063"></a>00063   input_cin &gt;&gt; num_nodes_x; 
<a name="l00064"></a>00064   input_cin &gt;&gt; num_nodes_y; 
<a name="l00065"></a>00065   input_cin &gt;&gt; Amp; 
<a name="l00066"></a>00066   input_cin &gt;&gt; tdma_iter;
<a name="l00067"></a>00067   input_cin &gt;&gt; tolerance;
<a name="l00068"></a>00068   input_cin.close();
<a name="l00069"></a>00069 
<a name="l00070"></a>00070   std::cout.precision(10);
<a name="l00071"></a>00071   std::cout.setf(ios_base::fixed,ios_base::floatfield);
<a name="l00072"></a>00072 
<a name="l00073"></a>00073   <a class="code" href="classTuna_1_1StructuredMesh.html" title="General structured meshes on rectangular domains.">StructuredMesh&lt;Uniform&lt;double, 2&gt;</a> &gt; mesh(length_x, num_nodes_x,
<a name="l00074"></a>00074                                            length_y, num_nodes_y);
<a name="l00075"></a>00075   <span class="keywordtype">double</span> dx = mesh.getDelta(X);
<a name="l00076"></a>00076   <span class="keywordtype">double</span> dy = mesh.getDelta(Y);
<a name="l00077"></a>00077   mesh.print();
<a name="l00078"></a>00078 
<a name="l00079"></a>00079   ScalarField2D T (mesh.getExtentVolumes());
<a name="l00080"></a>00080   ScalarField2D Ta(mesh.getExtentVolumes());
<a name="l00081"></a>00081   ScalarField2D Tn(mesh.getExtentNodes());
<a name="l00082"></a>00082   
<a name="l00083"></a>00083   Range all = Range::all();
<a name="l00084"></a>00084 
<a name="l00085"></a>00085   firstIndex i;
<a name="l00086"></a>00086   Range I(Tn.lbound(firstDim), Tn.ubound(firstDim));
<a name="l00087"></a>00087   Tn(I, Tn.lbound(secondDim)) = 100 * sin( PI * dx * i/ length_x);
<a name="l00088"></a>00088   InOut::writeToFile(Tn, 0, <span class="stringliteral">&quot;./DataHoffman/temp.&quot;</span>, dx, dy);
<a name="l00089"></a>00089   NumUtils::interpolateToVolumes(T, Tn);
<a name="l00090"></a>00090   
<a name="l00091"></a>00091   exactSolution(Tn, length_x, length_y, Amp, dx, dy);
<a name="l00092"></a>00092   InOut::writeToFile(Tn, 0, <span class="stringliteral">&quot;./DataHoffman/exac.&quot;</span>, dx, dy);
<a name="l00093"></a>00093   NumUtils::interpolateToVolumes(Ta, Tn);
<a name="l00094"></a>00094  
<a name="l00095"></a>00095 <span class="preprocessor">#ifdef WITH_GNUPLOT</span>
<a name="l00096"></a>00096 <span class="preprocessor"></span>    GNUplot plotter;
<a name="l00097"></a>00097     plotter(<span class="stringliteral">&quot;set grid&quot;</span>);
<a name="l00098"></a>00098     plotter(<span class="stringliteral">&quot;set contour&quot;</span>);
<a name="l00099"></a>00099     plotter(<span class="stringliteral">&quot;set view 60,45,1,1&quot;</span>);
<a name="l00100"></a>00100     plotter(<span class="stringliteral">&quot;set ticslevel 1.5&quot;</span>);
<a name="l00101"></a>00101     plotter(<span class="stringliteral">&quot;set cntrparam level discrete 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95&quot;</span>);
<a name="l00102"></a>00102     plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/exac.00000\&quot; title \&quot;Exact solution\&quot; w l&quot;</span>);
<a name="l00103"></a>00103     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00104"></a>00104     <span class="keywordtype">int</span> pause; std::cin &gt;&gt; pause;
<a name="l00105"></a>00105     plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/temp.00000\&quot; title \&quot;Initial conditions\&quot;w l&quot;</span>);
<a name="l00106"></a>00106     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00107"></a>00107     std::cin &gt;&gt; pause;
<a name="l00108"></a>00108 <span class="preprocessor">#endif</span>
<a name="l00109"></a>00109 <span class="preprocessor"></span>
<a name="l00110"></a>00110     SparseMatrix&lt; Diagonal&lt;double, 2&gt; &gt; A(num_nodes_x, num_nodes_y); 
<a name="l00111"></a>00111 
<a name="l00112"></a>00112     ScalarField2D             b(num_nodes_x, num_nodes_y);
<a name="l00113"></a>00113   
<a name="l00114"></a>00114     <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp;amp; N trick.">ScalarEquation&lt; LaplaceScheme&lt;double, 2&gt;</a> &gt; laplace(T, A, b,
<a name="l00115"></a>00115                                                        mesh.getDeltas());
<a name="l00116"></a>00116     laplace.setDirichlet(TOP_WALL);
<a name="l00117"></a>00117     laplace.setDirichlet(BOTTOM_WALL);
<a name="l00118"></a>00118     laplace.setDirichlet(LEFT_WALL);
<a name="l00119"></a>00119     laplace.setDirichlet(RIGHT_WALL);
<a name="l00120"></a>00120     laplace.setGamma(1.0);
<a name="l00121"></a>00121     laplace.print();
<a name="l00122"></a>00122 
<a name="l00123"></a>00123     time.<a class="code" href="structTuna_1_1timer.html#a5b0cf85d5db9b941e13ce7c79d7de7b0" title="Start the clock.">tic</a>();        
<a name="l00124"></a>00124 
<a name="l00125"></a>00125     laplace.calcCoefficients();
<a name="l00126"></a>00126     <span class="keywordtype">int</span> iter = Solver::TDMA2DY(laplace, tolerance, tdma_iter);
<a name="l00127"></a>00127 
<a name="l00128"></a>00128     std::cout &lt;&lt; <span class="stringliteral">&quot;\n Elapsed time for solving Ax = b : &quot;</span> 
<a name="l00129"></a>00129               &lt;&lt; time.<a class="code" href="structTuna_1_1timer.html#a3796592dd5b589521e1093d9225eee5e" title="Stop the clock and returns the elapsed time.">toc</a>() &lt;&lt; <span class="stringliteral">&quot; seconds \n\n&quot;</span>;   
<a name="l00130"></a>00130     
<a name="l00131"></a>00131     std::cout &lt;&lt; <span class="stringliteral">&quot;\n Iterations = &quot;</span> &lt;&lt; iter
<a name="l00132"></a>00132               &lt;&lt; <span class="stringliteral">&quot;\t Residual = &quot;</span> &lt;&lt; laplace.getResidual();
<a name="l00133"></a>00133 
<a name="l00134"></a>00134     laplace.update();  
<a name="l00135"></a>00135     NumUtils::interpolateToNodes(Tn, T);
<a name="l00136"></a>00136     InOut::writeToFile(Tn, 1, <span class="stringliteral">&quot;./DataHoffman/temp.&quot;</span>, dx, dy);
<a name="l00137"></a>00137 
<a name="l00138"></a>00138     cout &lt;&lt; <span class="stringliteral">&quot;\t Error = &quot;</span> &lt;&lt; NumUtils::calcErrorL1( T, Ta ) &lt;&lt; endl;    
<a name="l00139"></a>00139        
<a name="l00140"></a>00140     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt;= T.ubound(firstDim); ++i)
<a name="l00141"></a>00141       <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j &lt;= T.ubound(secondDim); ++j) 
<a name="l00142"></a>00142         T(i,j) = abs(T(i,j) - Ta(i,j));
<a name="l00143"></a>00143 
<a name="l00144"></a>00144 
<a name="l00145"></a>00145 
<a name="l00146"></a>00146 
<a name="l00147"></a>00147     NumUtils::interpolateToNodes(Tn, T);           
<a name="l00148"></a>00148     InOut::writeToFile(Tn, 0, <span class="stringliteral">&quot;./DataHoffman/erro.&quot;</span>, dx, dy);
<a name="l00149"></a>00149 
<a name="l00150"></a>00150 <span class="preprocessor">#ifdef WITH_GNUPLOT</span>
<a name="l00151"></a>00151 <span class="preprocessor"></span>    plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/temp.00001\&quot; title \&quot;Numerical Solution\&quot; w l&quot;</span>);
<a name="l00152"></a>00152     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00153"></a>00153     std::cin &gt;&gt; pause;
<a name="l00154"></a>00154     plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/erro.00000\&quot; title \&quot;Error\&quot; w l&quot;</span>);
<a name="l00155"></a>00155     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00156"></a>00156     std::cin &gt;&gt; pause;
<a name="l00157"></a>00157 <span class="preprocessor">#endif</span>
<a name="l00158"></a>00158 <span class="preprocessor"></span>    
<a name="l00159"></a>00159     <span class="keywordflow">return</span> 0;
<a name="l00160"></a>00160 }
<a name="l00161"></a>00161 
<a name="l00162"></a>00162 
<a name="l00163"></a>00163 
<a name="l00164"></a>00164 
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